Abstract

This paper discusses some of the basic problems involved in designing and using a magnetometer employing optical pumping. Particular attention is given to magnetometers of the self-oscillating type; i.e., those that are analogous to masers in that the resonant properties of the spin system itself are used to sustain continuous oscillation at the resonant frequency. Among the topics treated are amplitude variations with orientation, sensitivity, behavior in extremely weak magnetic fields, and response to rapid field changes.

© 1962 Optical Society of America

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References

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  1. H. G. Dehmelt, Phys. Rev. 105, 1487, 1924 (1957).
    [CrossRef]
  2. W. E. Bell, A. L. Bloom, Phys. Rev. 107, 1559 (1957), hereinafter referred to as I.
    [CrossRef]
  3. W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
    [CrossRef]
  4. F. Bloch, Phys. Rev. 70, 460 (1946).
    [CrossRef]
  5. W. E. Bell, A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
    [CrossRef]
  6. R. G. Aldrich, Thesis, U.S. Naval Postgraduate School, Monterey, 1961 (unpublished).
  7. T. L. Skillman, P. L. Bender, J. Geophys. Res. 63, 513 (1958); L. Malnar, J. P. Mosnier, Ann. Radioelec. 16, No. 63, 3 (1961).
    [CrossRef]
  8. F. Bloch, A. J. F. Siegert, Phys. Rev. 57, 522 (1940).
    [CrossRef]
  9. J. R. Singer, S. Wang, Phys. Rev. Letters 6, 351 (1961).
    [CrossRef]

1961

W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
[CrossRef]

W. E. Bell, A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[CrossRef]

J. R. Singer, S. Wang, Phys. Rev. Letters 6, 351 (1961).
[CrossRef]

1958

T. L. Skillman, P. L. Bender, J. Geophys. Res. 63, 513 (1958); L. Malnar, J. P. Mosnier, Ann. Radioelec. 16, No. 63, 3 (1961).
[CrossRef]

1957

H. G. Dehmelt, Phys. Rev. 105, 1487, 1924 (1957).
[CrossRef]

W. E. Bell, A. L. Bloom, Phys. Rev. 107, 1559 (1957), hereinafter referred to as I.
[CrossRef]

1946

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

1940

F. Bloch, A. J. F. Siegert, Phys. Rev. 57, 522 (1940).
[CrossRef]

Aldrich, R. G.

R. G. Aldrich, Thesis, U.S. Naval Postgraduate School, Monterey, 1961 (unpublished).

Bell, W. E.

W. E. Bell, A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[CrossRef]

W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
[CrossRef]

W. E. Bell, A. L. Bloom, Phys. Rev. 107, 1559 (1957), hereinafter referred to as I.
[CrossRef]

Bender, P. L.

T. L. Skillman, P. L. Bender, J. Geophys. Res. 63, 513 (1958); L. Malnar, J. P. Mosnier, Ann. Radioelec. 16, No. 63, 3 (1961).
[CrossRef]

Bloch, F.

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

F. Bloch, A. J. F. Siegert, Phys. Rev. 57, 522 (1940).
[CrossRef]

Bloom, A. L.

W. E. Bell, A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[CrossRef]

W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
[CrossRef]

W. E. Bell, A. L. Bloom, Phys. Rev. 107, 1559 (1957), hereinafter referred to as I.
[CrossRef]

Dehmelt, H. G.

H. G. Dehmelt, Phys. Rev. 105, 1487, 1924 (1957).
[CrossRef]

Lynch, J.

W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
[CrossRef]

Siegert, A. J. F.

F. Bloch, A. J. F. Siegert, Phys. Rev. 57, 522 (1940).
[CrossRef]

Singer, J. R.

J. R. Singer, S. Wang, Phys. Rev. Letters 6, 351 (1961).
[CrossRef]

Skillman, T. L.

T. L. Skillman, P. L. Bender, J. Geophys. Res. 63, 513 (1958); L. Malnar, J. P. Mosnier, Ann. Radioelec. 16, No. 63, 3 (1961).
[CrossRef]

Wang, S.

J. R. Singer, S. Wang, Phys. Rev. Letters 6, 351 (1961).
[CrossRef]

J. Geophys. Res.

T. L. Skillman, P. L. Bender, J. Geophys. Res. 63, 513 (1958); L. Malnar, J. P. Mosnier, Ann. Radioelec. 16, No. 63, 3 (1961).
[CrossRef]

Phys. Rev.

F. Bloch, A. J. F. Siegert, Phys. Rev. 57, 522 (1940).
[CrossRef]

H. G. Dehmelt, Phys. Rev. 105, 1487, 1924 (1957).
[CrossRef]

W. E. Bell, A. L. Bloom, Phys. Rev. 107, 1559 (1957), hereinafter referred to as I.
[CrossRef]

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

Phys. Rev. Letters

W. E. Bell, A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[CrossRef]

J. R. Singer, S. Wang, Phys. Rev. Letters 6, 351 (1961).
[CrossRef]

Rev. Sci. Instr.

W. E. Bell, A. L. Bloom, J. Lynch, Rev. Sci. Instr. 32, 688 (1961).
[CrossRef]

Other

R. G. Aldrich, Thesis, U.S. Naval Postgraduate School, Monterey, 1961 (unpublished).

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Figures (7)

Fig. 1
Fig. 1

Differential probability of obtaining a signal of amplitude S. Curve A: S = cos2θ and S = sinθ cosθ. Curve B: S = sin2θ.

Fig. 2
Fig. 2

Block diagram of magnetometer employing Mz signal and phase detector to stabilize a local oscillator at the Larmor frequency. Minor variations of this scheme may employ magnetic field sweep, low-frequency offset oscillators, or servo loops responsive only within a certain range of frequencies.

Fig. 3
Fig. 3

Self-oscillator type of magnetometer employing a single absorption cell.

Fig. 4
Fig. 4

Signal amplitude or signal-to-noise ratio of the self-oscillator as a function of θ. These curves differ from the simple sinθ cosθ dependence in that they include the effect of variation of the perpendicular component of the rf field. K = γHa(T1T2)½ where 2Ha is the peak value of the alternating rf field along the coil axis.

Fig. 5
Fig. 5

Self-oscillator employing two absorption cells. If the two optical systems are placed back-to-back, as shown, then the two circular polarizers should be of the same sense (e.g., right-handed) to preserve symmetry upon 180° rotation.

Fig. 6
Fig. 6

Phase shift in the photocell signal as a function of orientation angle, θ, shown for three misorientation angles of the rf coil axis relative to the optical axis.

Fig. 7
Fig. 7

Analog computer curves showing response of self-oscillator system to relatively large and rapid magnetic field transients.

Tables (1)

Tables Icon

Table I Splitting of the Zeeman Resonance in a Field of 0.5 Gaussa

Equations (14)

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d P ( θ ) / d θ = sin θ ,
d P d S = d P ( θ ) / d θ d S ( θ ) / d θ
d P d S = 1 2 S
d P d S = 1 2 ( 1 S )
Γ = Γ r + Γ t
N = ( 2 e 2 n B ) 1 / 2
N ( Γ Γ r ) 1 / 2 .
S Γ r 2 / Γ .
S N Γ = Γ r 3 / 2 ( Γ r + Γ t ) 5 / 2 .
M z + i M y = n = f n e i n w t , M z = n = m n e i n w t .
M osc = M x sin θ + ( M z ) 1 cos θ , M x = γ H 1 M 0 [ ω 0 + ω T 2 2 + ( ω 0 + ω ) 2 + ω 0 ω T 2 2 + ( ω 0 ω ) 2 ] cos ω t γ H 1 M 0 T 2 [ 1 T 2 2 + ( ω 0 + ω ) 2 1 T 2 2 + ( ω 0 ω ) 2 ] sin ω t , ( M z ) 1 = 2 γ H 1 T 1 T 2 ω 0 M 0 ( cos ω t ω T 2 sin ω t ) ( 1 + T 1 2 ω 2 ) ( 1 + T 2 2 ω 0 2 ) .
ω = [ ( 1 / T 2 ) 2 + ω 0 2 ] 1 / 2 .
δ ω = γ H 1 2 / 4 H 0 .
φ = tan 1 ( M y / M x )

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